Protesters at the Lindsey oil refinery in North Lincolnshire. Photograph: Anna Gowthorpe/PA

Gordon Brown has no regrets over using the phrase "British jobs for British workers", Downing Street insisted today as a series of unofficial strikes broke out over UK construction jobs awarded to European workers.

As anger intensified over plans by oil companies to employ Portuguese and Italian workers, the prime minister said that he understood people's concerns.

Asked whether the prime minister regretted using the controversial phrase, branded illegal and racist by critics, his spokesman in London said: "I don't see any reason for regret. The action that we have taken has meant that we are now putting in place measures that ensure British workers can have access to the vacancies in the system."

Some of the workers who walked out at refineries and power stations in various parts of the UK held placards quoting the prime minister's words. The wildcat strikes mark the latest in a series of protests over the use of foreign rather than domestic labour by large companies.

Asked about the situation in Davos, Brown said: "I understand people's worries about their jobs. I understand people's anxieties about employment across the country. But we are doing everything we can both to get economic growth moving in our country and to help people who are unemployed, to help them into new jobs."

In London, the Downing Street spokesman said the government understood that contracts for the construction work in question were awarded "some time ago when there was a shortage of skilled labour in the UK", and added: "That's obviously not now the case."

The spokesman said ministers would be "speaking to the industry in the next few days to ensure they did all they can to help the British economy".

Pressed on the matter, the spokesman was unable to say what meeting had been set up or with whom. He could not say which government department was leading the negotiations.

He insisted ministers were doing all they could to shore up the economy, and said: "What we have tried to do with the points-based [immigration] system is ensure that British workers are given the opportunities that exist in the labour market first."

More than 700 BP and Ineos workers at the Grangemouth oil refinery in Scotland walked out this morning after an 8am union meeting. Police were called to the Aberthaw power station near Barry, south Wales, and 400 workers at a refinery in Wilton, near Redcar, Teesside, downed tools.

In Davos, the prime minister said: "I came into politics to help people out of unemployment, to help people who were poor by building an economy that was confident and strong to weather this storm. I believe that the action we have taken to help people in work stay in work, to help people who lose their jobs get jobs again ... is the way to do it."